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Why math is painful to read

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Re: Why math is painful to read

#101

Post by Someone »

davegauer wrote: post #34
michaelochurch wrote: post #10

Disagree strongly. Math is often the easiest and simplest thing that works for the class of problems it exists to solve. Imagine trying to explain singular value decomposition without the notion of a matrix. No group theory, no well-formed concept of a linear transformation or function . You wouldn't be able to do it. No one even had such ideas before generations of mathematical machinery had been built. I've come to…

I think you make a really good point about the power of mathematical notation and conventions. However, I completely agree with the article. Do mathematical formulas have to use Greek letters rather than useful variable names like "distance" or "speed"? Does C's syntax actually allow you to express something you can't in Python? Or is it more terse for historical reasons? (And never mind that it's a good idea to use…

Do mathematical formulas have to use Greek letters rather than useful variable names like "distance" or "speed"?

The moment you are talking 'distance' and 'speed', you are talking physics (aka applied mathematics), not mathematics.

The same math might see applications in economics, where the variables are better called 'piggy bank target' and 'weekly savings', or in biology, where they call them 'weight needed to survive the winter' and 'excess food intake' or elsewhere in physics, where they are called 'velocity' and 'acceleration'.

Mathematics is abstraction; that is what makes it applicable in diverse fields.

Re: Why math is painful to read

#102

Post by kd0amg »

trhtrsh wrote: post #93
kd0amg wrote: post #82

Earlier quoted context omitted.

If a non-programmer asks you "Why do you guys say int x = 10; float y = 0.2 Why not x is an whole number who value is 10 y is a fraction whose value is one fifth. Knowing what language we're working in is enough to know that's exactly what that code says. This is not the case in mathematical notation. C × A could be the direct product of two groups, or maybe the tensor product of two graphs, or perhaps the product of…

Knowing what language we're working in is enough to know that's exactly what that _math_ says, too. You don't expect to understand Java after learning PHP, and you don't expect to understand a Topology paper after learning Algebra. "C x A" is a combination of C and A. C, x, and A are defined once somewhere at the beginning of the paper/book.

"C x A" is a combination of C and A. C, x, and A are defined once somewhere at the beginning of the paper/book.

Should I take this (which doesn't actually hold in the general case) to mean that every document uses its own language? That isn't exactly good for readability. We certainly don't consider every software project to be written in its own language (and no, the semantics of C does not tell us what the dP function does).

Re: Why math is painful to read

#103

Post by kd0amg »

Xcelerate wrote: post #68
dxbydt wrote: post #23

Frankly, there are 2 kinds of programmers. People who do this: val result = directProduct(cyclicGroupOfDegree3, finiteAbelianGroupOfDegree7) and the second kind, people like me, who do this: // Compute the direct product of 2 cyclic groups val z = dP( cg1, cg2 ) You can easily guess that the 2nd kind are math majors. If my math professor started writing everything out in plain English like the first example, he'd nev…

To me, I highly prefer the first expression you've written (well, without the exaggerated style you've given it). The second may save you some time in the short run, but when you come back to your code in a year, you think you'll know what dP means? Differential of P? Distance to P? Distance from P? I realize you've got a comment above it, but if you really code like that then you are very different from any code I'v…

(Also, I don't think all math majors use that second style).

Indeed. I don't, and I can think of several others who don't. Then again, most of the math majors I know were/are also studying CS.

Re: Why math is painful to read

#104

Post by glomph »

tokenadult wrote: post #5

The article "How to Write Mathematics" http://www.math.uga.edu/~azoff/courses/halmos.pdf by the late Paul Halmos, a mathematician famous for his clarity of writing, suggests procedures for making mathematical papers less painful to read.

Really enjoyed some of that. Thanks.

Re: Why math is painful to read

#105

Post by gfodor »

trhtrsh wrote: post #94
gfodor wrote: post #38

The problem with math isn't symbology or notation per se, it's that it's not evolved to take advantage of modern technology. It's an artifact of pencil-and-paper being the medium of choice for expressing ideas. We can do much better. When you are looking at an equation, you are looking at the purest distillation of an idea. Underneath that equation sits countless layers of abstraction and reasoning. Why can't I peel…

Math's hyperlink: http://mathworld.wolfram.com/Angle.html

not following?

Re: Why math is painful to read

#106

Post by norswap »

kd0amg wrote: post #85
norswap wrote: post #24

I agree. I always felt that if math theorems were presented in a programming language, they would be way more understandable (especially if the good practices are respected: meaningful variable names, etc). Mathematicians love to talk about rigor, but when it comes down to write their ideas, they often have little enough of it.

I always felt that if math theorems were presented in a programming language, they would be way more understandable …. Find out empirically! Look at theorems in some formal methods/programming languages papers and their corresponding mechanizations and see which you find more understandable. (Actually, it might be better to start with something like Software Foundations to get a gentler introduction to a programming…

Hard to do, the one you will look at second will always be at an advantage. So you'd have to select two theorems of "equivalent difficulty", which is not easy. Also you need to select hard to understand theorems, else you'll understand both the representations easily anyway.
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